Synthetic division is based on the mathematical findings of mathematician Paolo Ruffini. It is also called division through Ruffini's Rule, but other variants exist, such as Horner's Method.
Synthetic division is a faster way to divide two polynomials than using long division. It takes the coefficients of both polynomials, the dividend and divisor, to create two sets of numbers. These coefficients are then multiplied strategically in sequences, and the products are written diagonally. The products are then added to the coefficient columns of the dividend. The results then become the coefficients of the quotient polynomial, which is the answer. Horner's Method is another way to evaluate polynomials using coefficients. It is also considered synthetic division.